Mixed-strategy minimax theorem without compactness

The authors establish a new mixed-strategy minimax theorem for a two-person zero-sum game given in the normal form f:X×Y → R. This is interpreted in the usual way, so that if the minimizer picks a pure strategy x in X and the maximizer picks a pure strategy y in Y then the payoff (to the maximizer) is f(x, y). It is assumed that the pure strategy space X is a compact Hausdorff space, and that the mixed strategies available to the minimizer are the regular Borel probability measures on X, collectively denoted by B(X). The approach is asymmetric in that it is not assumed that the maximizer's pure strategies are necessarily topologized.